AQA · GCSE · Combined Science
Course version: 8464 · Version from Sept 2018
Density of materials: density = mass / volume
Density tells you how much mass is packed into each unit of volume.
Study notes
From the checked teaching notes for this specification point.
The idea
Density tells you how much mass is packed into each unit of volume. The relationship density = mass / volume means that for a uniform material, dividing the mass in kilograms by the volume in cubic metres gives the density in kilograms per cubic metre. For example, a 2.0 kg block of volume 0.0010 m³ has density 2.0 ÷ 0.0010 = 2000 kg/m³. Rearranged, mass = density × volume and volume = mass ÷ density. In practice you measure mass with a balance and volume by measuring dimensions of a regular solid, or by displacement of water for an irregular solid. The equation applies to a uniform material; a hollow object has a lower average density than the solid material it is made from.
What earns the marks
- State the relationship as density = mass ÷ volume and identify the correct quantities from the question.
- Substitute values with consistent units, converting grams to kilograms and cm³ to m³ where necessary.
- Calculate correctly and give the unit as kg/m³, or g/cm³ if the question uses those units.
- Rearrange the equation to find mass or volume when density and one other quantity are given.
- Interpret a calculated density, for example by comparing it with a known value or explaining floating and sinking.
Common mistakes and how to put them right
Dividing volume by mass instead of mass by volume.
Put it right by checking that density is larger for a given mass when volume is smaller.
Mixing units, such as using grams with cubic metres.
Put it right: Convert all values to kilograms and cubic metres before dividing.
Forgetting to cube a length when finding volume of a cube.
Put it right: If side = 2 cm, volume = 2³ = 8 cm³, not 6 cm³.
Exam tips
- Write the equation, then substitute numbers with units before calculating so method marks can be awarded.
- Check whether the question expects kg/m³ or g/cm³ and convert if needed; 1 g/cm³ = 1000 kg/m³.
- For irregular solids, describe measuring volume by displacement and subtracting the initial water reading.
Try the lesson
The start of the Density of materials: density = mass / volume lesson, made from checked teaching notes for this specification point.
Have a go first
A block of wood has a mass of 240 g and a volume of 300 cm³. Use density = mass / volume to calculate the density of the wood in g/cm³.
Listen
Density tells you how much mass is packed into each unit of volume. The relationship density = mass / volume means that for a uniform material, dividing the mass in kilograms by the volume in cubic metres gives the density in kilograms per cubic metre. For example, a 2.0 kg block of volume 0.0010 m³ has density 2.0 ÷ 0.0010 = 2000 kg/m³. Rearranged, mass = density × volume and volume = mass ÷ density. In practice you measure mass with a balance and volume by measuring dimensions of a regular solid, or by displacement of water for an irregular solid. The equation applies to a uniform material; a hollow object has a lower average density than the solid material it is made from. A strong answer earns marks for these points. State the relationship as density = mass ÷ volume and identify the correct quantities from the question. Substitute values with consistent units, converting grams to kilograms and cm³ to m³ where necessary. Calculate correctly and give the unit as kg/m³, or g/cm³ if the question uses those units. Rearrange the equation to find mass or volume when density and one other quantity are given. A common slip: Dividing volume by mass instead of mass by volume. Instead, checking that density is larger for a given mass when volume is smaller. Exam tip: Write the equation, then substitute numbers with units before calculating so method marks can be awarded.
There is more to this lesson
The full lesson goes on to check your understanding and help you earn the marks. Create a free account to carry on, with your progress saved.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge
Test your understanding of Density of materials: density = mass / volume
Active recall beats re-reading. Take an instant quiz now to test what you’ve learned and lock it into long-term memory.
A week of Premium from your first lesson · Then the free plan continues · No card, no charge